BOSTON—Gabriel Krause-Grosman, 12 years old, spent family dinners for the greater part of a year on a smartphone offensive. He hounded. He pleaded. All his friends had one, he prodded. Yet his parents stood firm.

“Who the hell would give a junior-high schoolchild a gaming platform to walk through the world with?” said Ellen Krause-Grosman, his mother. “It feels a little like trying to teach your kid how to use cocaine, but in a balanced way.”